Combining branching processes and Allee effects into an integral projection model to assess invasion risk

Invasive species threaten both ecological systems and economies. Successful establishment is governed partly by demographic stochasticity, where random individual-level variation can significantly influence invasion dynamics. A critical factor is the Allee effect, which describes reduced population growth at low densities, potentially serving as a barrier to persistence. Size-dependent growth and survival further shape outcomes based on the size distribution of individuals within the population. To address these complexities, we developed a population-level model integrating an Integral Projection Model (IPM) for the expected size distribution with an Allee effect for recruitment dynamics and a branching process to account for demographic stochasticity. We applied this framework to Silver Carp ( Hypophthalmichthys molitrix ), a species established in the Upper Mississippi River system that poses significant risk of expanding into the Great Lakes. Our analysis compared temporal dynamics and population-size distributions under hypothetical introduction scenarios for large adult and smaller subadult fish. In both cases, initial population size relative to the Allee threshold was a critical determinant of establishment probability, with introductions below the threshold requiring stochastic growth across a critical biomass boundary before self-sustaining dynamics could take hold. Sensitivity analysis further indicated that per-spawner recruitment played a compounding role in invasion risk: higher recruitment rates reduced the critical introduction size for establishment and compressed the time to self-sustaining population size, jointly broadening the window of invasion risk. These findings highlight the framework’s potential for invasion assessments and offer insights into how Allee effects, size structure, and recruitment rates interact to govern establishment outcomes, while underscoring the need for species-specific parameter estimates before quantitative outputs can guide management decisions.